Definitely a knockdown texture. :yes:
Which is sprayed on by several different methods, from a truck mounted texture rig all the way down to a hand held hopper gun and air compressor.
By the looks of that knockdown texture, it was probably sprayed on with a hopper.
The problem with trying to spray KD texture with a hopper is the material that is used is heavy and the hopper and air compressor don't have enough umph to throw the material up to a ceiling. So then the person spraying the texture tries to fix the problem by adding more water to the mix making it soupy. Resulting in a more flattened out Knockdown like in pic 2.
So I would think using a spray can of knockdown texture (Which I personally don't like because it comes out too thin for ceiling repairs) or even a knockdown texture sponge to blend the texture might be the best method for a DIY 'er. :thumbup:
Here's a video of me using the knockdown sponge on a vaulted ceiling repair:
Ps. The mud work on your drywall ceiling repair in the pic is going to need a couple more coats of mud.